“…Continuing with our analysis of mechanical properties, we can also compare the BGY predictions with experimental data for the volume change on mixing. This is illustrated in Figure which shows results for Δ V mix over the entire composition range with P = 0.1 MPa and the temperature ranging from 293 to 323 K. − Recall that the BGY predictions are calculated using pure component data alone, making use of eq 1 for the mixed interaction energy. Note that the values for Δ V mix are very small, being on the order of 10 -4 L mol -1 , while the molar volumes of the mixtures are on the order of 10 -1 L mol -1 .…”
Section: Mixtures Of N-alkanesmentioning
confidence: 99%
“… 4 Volume change on mixing as a function of composition for n- C6/ n -C16 at a series of temperatures. The solid lines are the BGY predictions for temperatures (from top to bottom) 293.15, 313.15, 323.15, and 333.15 K. The symbols are the corresponding experimental results from a variety of studies: filled symbols, ref ; open circles and squares, ref ; open triangles, ref ; dotted circles, ref ; dotted squares, ref . 5 Volume change on mixing as a function of composition (mole fraction of lowest alkane) at 298.15 K and atmospheric pressure for n -C6/ n -C8 (diamonds 33a ), n -C8/ n -C12 (squares 33b ), and n -C6/ n -C12 (circles 32 ).…”
Section: Mixtures Of N-alkanesmentioning
confidence: 99%
“…We begin by examining several n -alkane solutions, particularly the hexane−hexadecane mixture as that has been the most widely studied experimentally. Since we have had some success in using pressure−volume−temperature ( PVT ) data, we start by considering the PVT surface of the mixture , and then turn to other thermodynamic quantities of interest, such as the volume change on mixing − and the equilibrium vapor pressure above the mixture. , For the polyethylene− n -alkane solutions we are primarily interested in the coexistence curve and its extremum, the LCST. ,,, While it may not be realistic to expect quantitative agreement between experiment and theory over the entire range of experimental conditions, it is possible to test the ability of a theory to make predictions about trends.…”
We have applied the lattice Born−Green−Yvon theory to the study of hydrocarbon mixtures.
In doing so we have fit pure component data in order to determine characteristic parameters for the
pure fluids and have used the geometric mean approximation for the mixed-segment interaction energy.
As a result, we have been able to make predictions for a wide variety of solution properties without
fitting any data on the mixtures and have compared our predictions with experimental results. For binary
alkane solutions made from combinations of n-hexane, n-octane, n-decane, and n-hexadecane we have
found excellent agreement between theory and experiment for pressure−volume isotherms, volume
changes on mixing and its pressure dependence, and equilibrium solution vapor pressures as a function
of composition and temperature. For polyethylene−n-alkane solutions we have been able to predict the
lower critical solution temperature and its dependence on the chain length of the alkane solvent, as well
as the full coexistence curve and its variation with the polymer molecular weight.
“…Continuing with our analysis of mechanical properties, we can also compare the BGY predictions with experimental data for the volume change on mixing. This is illustrated in Figure which shows results for Δ V mix over the entire composition range with P = 0.1 MPa and the temperature ranging from 293 to 323 K. − Recall that the BGY predictions are calculated using pure component data alone, making use of eq 1 for the mixed interaction energy. Note that the values for Δ V mix are very small, being on the order of 10 -4 L mol -1 , while the molar volumes of the mixtures are on the order of 10 -1 L mol -1 .…”
Section: Mixtures Of N-alkanesmentioning
confidence: 99%
“… 4 Volume change on mixing as a function of composition for n- C6/ n -C16 at a series of temperatures. The solid lines are the BGY predictions for temperatures (from top to bottom) 293.15, 313.15, 323.15, and 333.15 K. The symbols are the corresponding experimental results from a variety of studies: filled symbols, ref ; open circles and squares, ref ; open triangles, ref ; dotted circles, ref ; dotted squares, ref . 5 Volume change on mixing as a function of composition (mole fraction of lowest alkane) at 298.15 K and atmospheric pressure for n -C6/ n -C8 (diamonds 33a ), n -C8/ n -C12 (squares 33b ), and n -C6/ n -C12 (circles 32 ).…”
Section: Mixtures Of N-alkanesmentioning
confidence: 99%
“…We begin by examining several n -alkane solutions, particularly the hexane−hexadecane mixture as that has been the most widely studied experimentally. Since we have had some success in using pressure−volume−temperature ( PVT ) data, we start by considering the PVT surface of the mixture , and then turn to other thermodynamic quantities of interest, such as the volume change on mixing − and the equilibrium vapor pressure above the mixture. , For the polyethylene− n -alkane solutions we are primarily interested in the coexistence curve and its extremum, the LCST. ,,, While it may not be realistic to expect quantitative agreement between experiment and theory over the entire range of experimental conditions, it is possible to test the ability of a theory to make predictions about trends.…”
We have applied the lattice Born−Green−Yvon theory to the study of hydrocarbon mixtures.
In doing so we have fit pure component data in order to determine characteristic parameters for the
pure fluids and have used the geometric mean approximation for the mixed-segment interaction energy.
As a result, we have been able to make predictions for a wide variety of solution properties without
fitting any data on the mixtures and have compared our predictions with experimental results. For binary
alkane solutions made from combinations of n-hexane, n-octane, n-decane, and n-hexadecane we have
found excellent agreement between theory and experiment for pressure−volume isotherms, volume
changes on mixing and its pressure dependence, and equilibrium solution vapor pressures as a function
of composition and temperature. For polyethylene−n-alkane solutions we have been able to predict the
lower critical solution temperature and its dependence on the chain length of the alkane solvent, as well
as the full coexistence curve and its variation with the polymer molecular weight.
“…As far as we know, there are not any literature data available for the studied binary mixtures at these temperatures. A literature review shows that the thermodynamic properties of binary mixtures containing alcohols with either C 16 H 34 or C 30 H 62 are not well known [1][2][3][4][5], whereas those for binary mixtures of hydrocarbons with C 16 H 34 or C 30 H 62 are available in the literature [6][7][8][9][10][11][12][13][14][15][16][17][18]. So it offers us a good opportunity to study the mixing behavior in such systems.…”
Excess molar volumes, V E m , excess molar isentropic compressibilities, K E S,m , and deviations of the speeds of sound, u D , from their ideal values u id in an ideal mixture for binary mixtures of 1-octanol, C 8 H 17 OH, with hexadecane, C 16 H 34 , and squalane (2,6,10,15,19,23-hexamethyltetracosane), C 30 H 62 , at T = (298.15, 303.15, and 308.15) K and at atmospheric pressure were derived from experimental density, ρ, and speed-of-sound data, u. Viscosity measurements were also carried out for the same mixtures. The Prigogine-Flory-Patterson (PFP) theory has been applied to analyze V E m of these systems. Furthermore, the apparent molar volumes, V 0 ϕ,i and apparent molar compressibility, K 0 ϕ,i of the components at infinite dilution have been calculated.
“…This principle has been found to hold for n-alkane mixtures nearly within experimental uncertainty 2−4 and holds to a lesser extent with other alkane substituted homologous series such as n-alkan-1-ols. 5,6 In our earlier work, 7 the principle was shown to hold for the excess volumes of three and four component mixtures simulating hexane + hexadecane to within 1 % relative at V m E (max) for hexane + hexadecane. For the excess enthalpy with similar mixtures, the agreement was within 2 % relative at H m E (max).…”
Excess molar volumes of mixtures of cyclohexane and pseudocyclohexane (an equimolar mixture of cyclopentane + cycloheptane) with hexadecane and various pseudohexadecanes (equimolar mixtures of tetradecane + octadecane, decane + docosane, or octane + tetracosane) have been measured at 313.15 K. The results for the multicomponent mixtures are compared with those for the binary mixtures and they show that n-alkanes obey, not quite within experimental uncertainty, an extended principle of congruence with cyclohexane as the other component, whereas mixtures of pseudocyclohexane with hexadecane do not obey the extended principle.
■ INTRODUCTIONThe principle of congruence of Brønsted and Koefoed 1 states that the properties of a multicomponent n-alkane mixtures should depend only on the average carbon number of the mixture. For example, an n-alkane mixture of pentane (C 5 ) (1) + heptane (C 7 ) (2) with x 1+2 = 0.5 mixed with tetradecane (C 14 ) (3) + (1 − x) octadecane (C 18 ) (4) with x 3+4 = 0.5 should have the same excess volume, density, excess enthalpy, and excess Gibbs energy as an equimolar mixture of hexane (C 6 ) + hexadecane (C 16 ) and all mixtures should have the same density as undecane (C 11 ). This principle has been found to hold for n-alkane mixtures nearly within experimental uncertainty 2−4 and holds to a lesser extent with other alkane substituted homologous series such as n-alkan-1-ols. 5,6 In our earlier work, 7 the principle was shown to hold for the excess volumes of three and four component mixtures simulating hexane + hexadecane to within 1 % relative at V m E (max) for hexane + hexadecane. For the excess enthalpy with similar mixtures, the agreement was within 2 % relative at H m E (max). 7 Measurements have been made on mixtures of cycloalkanes with pseudocycoloalkanes by Letcher et al., 8 and it was concluded that cycloalkanes did not satisfy the principle of congruence to the same extent as n-alkanes. In this work, the hypothesis that an extended principle can be applied to pseudocycloalkane mixtures with n-alkanes was tested. Also tested was the hypothesis that a pseudo-n-alkane (for example an equimolar mixture of tetradecane + octadecane) behaves the same as hexadecane when mixed with an arbitrary second component.
■ EXPERIMENTAL SECTIONThe source and purity of the materials are summarized in Table 1. They were used without further purification except for passing through a column of activated alumina. The purities were determined with a Varian GLC using a flame ionization detector with a 20 m capillary SE-30 column with splitter. The pseudoalkanes and pseudocycloalkanes were prepared as described previously. 7 Briefly, the mixtures were prepared by mass in a flask containing a ground glass stopper with the mass of the less volatile component being determined first and then
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